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Performance evaluation of particular channel coding has been a significant topic in coding theory, often involving the use of bounding techniques. This paper focuses on the new family of capacity-achieving codes, Spinal codes, to provide a comprehensive analysis framework to tightly upper bound the block error rate (BLER) of Spinal codes in the finite block length (FBL) regime. First, we resort to a variant of the Gallager random coding bound to upper bound the BLER of Spinal codes over the fading channel. Then, this paper derives a new bound without resorting to the use of Gallager random coding bound, achieving provable tightness over the wide range of signal-to-noise ratios (SNR). The derived BLER upper bounds in this paper are generalized, facilitating the performance evaluations of Spinal codes over different types of fast fading channels. Over the Rayleigh, Nakagami-m, and Rician fading channels, this paper explicitly derived the BLER upper bounds on Spinal codes as case studies. Based on the bounds, we theoretically reveal that the tail transmission pattern (TTP) for ML-decoded Spinal codes remains optimal in terms of reliability performance. Simulations verify the tightness of the bounds and the insights obtained.

In this paper, we study a remote monitoring system where a receiver observes a remote binary Markov source and decides whether to sample and transmit the state through a randomly delayed channel. We adopt uncertainty of information (UoI), defined as the entropy conditional on past observations at the receiver, as a metric of value of information, in contrast to the traditional state-agnostic nonlinear age of information (AoI) penalty functions. To address the limitations of prior UoI research that assumes one-time-slot delays, we extend our analysis to scenarios with random delays. We model the problem as a partially observable Markov decision process (POMDP) problem and simplify it to a semi-Markov decision process (SMDP) by introducing the belief state. We propose two algorithms: A globally optimal bisection relative value iteration (bisec-RVI) algorithm and a computationally efficient sub-optimal index-based threshold algorithm to solve the long-term average UoI minimization problem. Numerical simulations demonstrate that our sampling policies surpass traditional zero wait and AoI-optimal policies, particularly under conditions of large delay, with the sub-optimal policy nearly matching the performance of the optimal one.

Age of Information (AoI) has been recognized as an important metric to measure the freshness of information. Central to this consensus is that minimizing AoI can enhance the freshness of information, thereby facilitating the accuracy of subsequent decision-making processes. However, to date the direct causal relationship that links AoI to the utility of the decision-making process is unexplored. To fill this gap, this paper provides a sampling-control co-design problem, referred to as an age-aware remote Markov Decision Process (MDP) problem, to explore this unexplored relationship. Our framework revisits the sampling problem in [1] with a refined focus: moving from AoI penalty minimization to directly optimizing goal-oriented remote decision-making process under random delay. We derive that the age-aware remote MDP problem can be reduced to a standard MDP problem without delays, and reveal that treating AoI solely as a metric for optimization is not optimal in achieving remote decision making. Instead, AoI can serve as important side information to facilitate remote decision making., Comment: 12 pages, 4 figures

Optimizations premised on open-loop metrics such as Age of Information (AoI) indirectly enhance the system's decision-making utility. We therefore propose a novel closed-loop metric named Goal-oriented Tensor (GoT) to directly quantify the impact of semantic mismatches on goal-oriented decision-making utility. Leveraging the GoT, we consider a sampler & decision-maker pair that works collaboratively and distributively to achieve a shared goal of communications. We formulate a two-agent infinite-horizon Decentralized Partially Observable Markov Decision Process (Dec-POMDP) to conjointly deduce the optimal deterministic sampling policy and decision-making policy. To circumvent the curse of dimensionality in obtaining an optimal deterministic joint policy through Brute-Force-Search, a sub-optimal yet computationally efficient algorithm is developed. This algorithm is predicated on the search for a Nash Equilibrium between the sampler and the decision-maker. Simulation results reveal that the proposed sampler & decision-maker co-design surpasses the current literature on AoI and its variants in terms of both goal achievement utility and sparse sampling rate, signifying progress in the semantics-conscious, goal-driven sparse sampling design., Comment: 30 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:2305.04083

The intricate interplay of source dynamics, unreliable channels, and staleness of information has long been recognized as a significant impediment for the receiver to achieve accurate, timely, and most importantly, goal-oriented decision making. Thus, a plethora of promising metrics, such as Age of Information, Value of Information, and Mean Square Error, have emerged to quantify these underlying adverse factors. Following this avenue, optimizing these metrics has indirectly improved the utility of goal-oriented decision making. Nevertheless, no metric has hitherto been expressly devised to evaluate the utility of a goal-oriented decision-making process. To this end, this paper investigates a novel performance metric, the Goal-oriented Tensor (GoT), to directly quantify the impact of semantic mismatches on the goal-oriented decision making. Based on the GoT, we consider a sampler-decision maker pair that work collaboratively and distributively to achieve a shared goal of communications. We formulate an infinite-horizon Decentralized Partially Observable Markov Decision Process (Dec-POMDP) to conjointly deduce the optimal deterministic sampling policy and decision-making policy. The simulation results reveal that the sampler-decision maker co-design surpasses the current literature on AoI and its variants in terms of both goal achievement utility and sparse sampling rate, signifying a notable accomplishment for a sparse sampler and goal-oriented decision maker co-design., Comment: 6 pages, 4, figures, Submitted to 2023 Globecom

Spinal codes, a family of rateless codes introduced in 2011, have been proved to achieve Shannon capacity over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we derive explicit tight upper bounds on the error probability of Spinal codes under maximum-likelihood (ML) decoding and perfect channel state information (CSI) over three typical fading channels, including the Rayleigh channel, the Nakagami-m channel and the Rician channel. Simulation results verify the tightness of the derived upper bounds.

The recent interweaving of AI-6G technologies has sparked extensive research interest in further enhancing reliable and timely communications. \emph{Age of Information} (AoI), as a novel and integrated metric implying the intricate trade-offs among reliability, latency, and update frequency, has been well-researched since its conception. This paper contributes new results in this area by employing a Deep Reinforcement Learning (DRL) approach to intelligently decide how to allocate power resources and when to retransmit in a \emph{freshness-sensitive} downlink multi-user Hybrid Automatic Repeat reQuest with Chase Combining (HARQ-CC) aided Non-Orthogonal Multiple Access (NOMA) network. Specifically, an AoI minimization problem is formulated as a Markov Decision Process (MDP) problem. Then, to achieve deterministic, age-optimal, and intelligent power allocations and retransmission decisions, the Double-Dueling-Deep Q Network (DQN) is adopted. Furthermore, a more flexible retransmission scheme, referred to as Retransmit-At-Will scheme, is proposed to further facilitate the timeliness of the HARQ-aided NOMA network. Simulation results verify the superiority of the proposed intelligent scheme and demonstrate the threshold structure of the retransmission policy. Also, answers to whether user pairing is necessary are discussed by extensive simulation results.

Since Shannon's pioneering masterpiece which established the prototype of modern information theory, the goal of communications has long been promising accurate message reconstruction at a refined bit-by-bit level, which deliberately neglects the semantics/effectiveness aspect of information. Nevertheless, the recent development of wireless technologies and the spurt of deep learning (DL) techniques allow us to reclaim the meaning/usefulness aspect in the design of future 6G communication paradigms, where goal-oriented communication is becoming a trend. Age of Information (AoI), a well-known metric that captures the importance of information by recording the time elapsed from the generation time slot, has been extended to various variants, such as Value of Information (VoI), Urgency of Information (UoI), Age of Incorrect Information (AoII), and etc. While each of them proposes novel ways to measure the meaning/usefulness aspect of information, there is not yet an integrated framework encompassing all of them. To this end, we propose a novel tensor-based approach, the Goal-oriented Tensor (GoT), to unify them, which also allows more flexible and fine-grained goal characterizations. Following the proposed GoT, we architect a holistic goal-oriented framework to enable goal-oriented semantic communications, in which information perception, dissemination, and control-plane decisions are implemented in accordance with specific goals. Finally, we outline several open challenges to fulfill the vision of the GoT framework.

Delivering timely status updates in a timeliness-critical communication system is of paramount importance to assist accurate and efficient decision making. Therefore, the topic of analyzing Age of Information has aroused new research interest. This paper contributes to new results in this area by systematically analyzing the AoI of two types of Hybrid Automatic Repeat reQuest (HARQ) techniques that have been newly standardized in the Release-16 5G New Radio (NR) specifications, namely reactive HARQ and proactive HARQ. Under a code-based status update system with non-trivial coding delay, transmission delay, propagation delay, decoding delay, and feedback delay, we derive unified closed-form average AoI and average Peak AoI expressions for reactive HARQ and proactive HARQ, respectively. Based on the obtained explicit expressions, we formulate an AoI minimization problem to investigate the age-optimal codeblock assignment strategy in the finite block-length (FBL) regime. Through case studies and analytical results, we provide comparative insights between reactive HARQ and proactive HARQ from a perspective of freshness of information. The numerical results and optimization solutions show that proactive HARQ draws its strength from both age performance and system robustness, thus enabling the potential to provide new system advancement of a freshness-critical status update system.